A Boundary Variation Diminishing Reconstructed Solver for Mie-Grüneisen Mixture Model

doi:10.19596/j.cnki.1001-246x.8712

Abstract

Abstract:

A numerical reconstruction is implemented according to a combination of MUSCL(Monotonic Upstream-Centered Scheme for Conservation Laws) and THINC(Tangent of Hyperbola for Interface Capturing) methods. And a new constructed solver is derived by the combination. The main principle of this reconstruction solver is to keep the variation diminishing of every cell boundary to a low level. And a BVD(Boundary Variation Diminishing) principle is set according to the left and right boundary states in MUSCL method, as well as which in THINC methods. To obey the BVD principle, an alternative choice between the MUSCL and THINC is needed here. Thanks to the BVD solver, the discontinuous section becomes smooth and the oscillation is significantly controlled. The numerical performance of BVD reconstruction is then tested by 1D and 2D numerical examples.

Key words: boundary variation diminishing(BVD) reconstruction, Mie-Grüneisen mixture model, monotonic upstream-centered scheme for conservation laws, tangent of hyperbola for interface capturing

CLC Number:

O359+.1

Zongduo WU, Jin YAN, Jianhua PANG, Yifang SUN, Qingyang MAN. A Boundary Variation Diminishing Reconstructed Solver for Mie-Grüneisen Mixture Model[J]. Chinese Journal of Computational Physics, 2024, 41(3): 277-286.

Figures/Tables 8

Fig.1 The grids property for MUSCL and THINC

Fig.2 Numerical solution of gas-water interaction

Fig.3 Numerical solution of gas-water interaction

Fig.4 Results of gaseous products and copper interaction

Fig.5 Variation dimishing distributions of basic variables (a) ρ, (b) ρu, (c) ρE in Euler formulation

Table 1 Hugoniot curve parameters for some materials

	ρ₀/(kg·m^-3)	c₀/(m·s^-1)	s	Г₀
Mo(钼)	9 961	4 700	1.43	1.56
MORB	2 660	2 100	1.68	0.18

Fig.6 Contours of pressure at (a) 50 μs and (b) 100 μs instant in molybdenum and MORB interaction

Fig.7 Pressure distributions along y=0.4 at (a) 50 μs and (b) 100 μs instant in molybdenum-MORB problem

References 24

1	任玉新, 陈海昕. 计算流体力学基础[M]. 北京: 清华大学出版社, 2006.
2	水鸿寿. 一维流体力学差分方法[M]. 北京: 国防工业出版社, 1998.
3	SHYUE K M . A wave-propagation based volume tracking method for compressible multicomponent flow in two space dimensions[J]. Journal of Computational Physics, 2006, 215 (1): 219- 244. DOI
4	SHYUE K M . A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state[J]. Journal of Computational Physics, 2001, 171 (2): 678- 707. DOI
5	吴宗铎, 严谨, 宗智, 等. 扩散界面形式下一种节约时间步的质量分数混合模型[J]. 计算物理, 2022, 39 (5): 510- 520. DOI
6	吴宗铎, 宗智. Mie-Grüneisen状态方程下多介质守恒型欧拉方程组的数值计算[J]. 计算物理, 2011, 28 (6): 803- 809. DOI
7	吴宗铎, 严谨, 宗智, 等. 一种基于HLLC算法的Mie-Grüneisen多介质混合模型[J]. 计算物理, 2020, 37 (1): 55- 62. DOI
8	WARD G M , PULLIN D I . A hybrid, center-difference, limiter method for simulations of compressible multicomponent flows with Mie-Grüneisen equation of state[J]. Journal of Computational Physics, 2010, 229 (8): 2999- 3018. DOI
9	HARTEN A . High resolution schemes for hyperbolic conservation laws[J]. Journal of Computational Physics, 1983, 49 (3): 357- 393. DOI
10	WU Zongduo , SUN Lei , ZONG Zhi . A mass-fraction-based interface-capturing method for multi-component flow[J]. International Journal for Numerical Methods in Fluids, 2013, 73 (1): 74- 102. DOI
11	SUN Ziyao , INABA S , XIAO Feng . Boundary variation diminishing (BVD) reconstruction: A new approach to improve godunov schemes[J]. Journal of Computational Physics, 2016, 322, 309- 325. DOI
12	肖锋. 基于BVD原理的高保真空间重构方法[J]. 空气动力学学报, 2021, 39 (1): 125- 137.
13	DENG Xi , INABA S , XIE Bin , et al. High fidelity discontinuity-resolving reconstruction for compressible multiphase flows with moving interfaces[J]. Journal of Computational Physics, 2018, 371, 945- 966. DOI
14	DENG Xi , SHIMIZU Yuya , XIAO Feng . A fifth-order shock capturing scheme with two-stage boundary variation diminishing algorithm[J]. Journal of Computational Physics, 2019, 386, 323- 349. DOI
15	DENG Xi , SHIMIZU Yuya , XIE Bin , et al. Constructing higher order discontinuity-capturing schemes with upwind-biased interpolations and boundary variation diminishing algorithm[J]. Computers & Fluids, 2020, 200, 104433.
16	RUAN Yucang , ZHANG Xinting , TIAN Baolin , et al. A flux split based finite-difference two-stage boundary variation diminishing scheme with application to the Euler equations[J]. Computers & Fluids, 2020, 213, 104725.
17	WAKIMURA H , TAKAGI S , XIAO Feng . Symmetry-preserving enforcement of low-dissipation method based on boundary variation diminishing principle[J]. Computers & Fluids, 2022, 233, 105227.
18	张昊, 谢春晖, 董义道, 等. 基于边界变差最小的高精度有限差分格式构造[J]. 航空学报, 2021, 42 (z1): 726397.
19	丁建中. MUSCL格式TV性质的非线性分析[J]. 计算物理, 1997, 14 (6): 782- 786.
20	BIDADI S , RANI S L . Investigation of numerical viscosities and dissipation rates of second-order TVD-MUSCL schemes for implicit large-eddy simulation[J]. Journal of Computational Physics, 2015, 281, 1003- 1031.
21	吴宗铎, 赵勇, 严谨, 等. 球坐标系下多介质混合物模型的数值模拟[J]. 爆炸与冲击, 2019, 39 (5): 054204.
22	BARTON P T . An interface-capturing Godunov method for the simulation of compressible solid-fluid problems[J]. Journal of Computational Physics, 2019, 390, 25- 50.
23	LIU Tiegang , KHOO B C , YEO K S . The simulation of compressible multi-medium flow. I. A new methodology with test applications to 1D gas-gas and gas-water cases[J]. Computers & Fluids, 2001, 30 (3): 291- 314.
24	SAUREL R , ABGRALL R . A multiphase Godunov method for compressible multifluid and multiphase flows[J]. Journal of Computational Physics, 1999, 150 (2): 425- 467.